Which of the following numbers is a multiple of 6? ${44,76,85,114,119}$
Solution: The multiples of $6$ are $6$ $12$ $18$ $24$ ..... In general, any number that leaves no remainder when divided by $6$ is considered a multiple of $6$ We can start by dividing each of our answer choices by $6$ $44 \div 6 = 7\text{ R }2$ $76 \div 6 = 12\text{ R }4$ $85 \div 6 = 14\text{ R }1$ $114 \div 6 = 19$ $119 \div 6 = 19\text{ R }5$ The only answer choice that leaves no remainder after the division is $114$ $ 19$ $6$ $114$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $114$ $114 = 2\times3\times19 6 = 2\times3$ Therefore the only multiple of $6$ out of our choices is $114$. We can say that $114$ is divisible by $6$.